Question #84641

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Answer 1 · 2017-04-02T09:19:06

6 hours

$Using visual assessment$ $color(blue)("Using visual assessment")$

Notice that the line intercepts the bottom axis at 9 and also the side axis at 9.

This condition is means that the value you select for one axis relates to the same value on the other axis.

Thus 3 hours watching TV relates to 6 hours sleeping.

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$Using mathematical assessment$ $color(blue)("Using mathematical assessment")$

One of the standardised forms for the equation of a strait line is:

$y = m x + c$ $y=mx+c$

where $m$ $m$ is the slope (gradient) and $c$ $c$ is the y-intercept.

By observation the y-intercept is 9 $\to y = m x + 9$ $->y=mx+9$

$m$ $m$ is the slope (gradient) reading left to right on the bottom axis

$m \to \frac{change in sleeping}{change in TV} \to \frac{0 - 9}{9 - 0} = - 1$ $m->("change in sleeping")/("change in TV") -> (0-9)/(9-0) =-1$

So we now have: $y = (- 1) x + 9 \to y = - x + 9$ $y=(-1)x+9" "->" "y=-x+9$

We need the value of $y$ $y$ when sleep is 3 hours

$y = - x + 9 \to y = - 3 + 9 = 6$ $y=-x+9" "->" "y=-3+9=6$

Tony B